The cost and size of an XFEL are driven mostly by the cost and size of the electron linear accelerator (linac). The electron beam in an XFEL must reach the energy above 10 GeV in order to generate radiation with wavelength below 1 \({_{\circ } \over {\mathrm {A}}}\)  with conventional undulators. The required beam energy translates into about 1 km-long accelerator built with conventional RF technology. Advanced accelerator concepts are currently under development and may provide solution for increasing accelerating gradients by several orders of magnitude [1]}, [2]}, [3]}, [4]}. So far, the most mature concept is acceleration of particles in a plasma wave [1]}, [2]}.
